Harvard AM205 video 5.6 - QR algorithm
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Жыл бұрынHarvard Applied Math 205 is a graduate-level course on scientific computing and numerical methods. This video introduces the QR algorithm, which can be used to find many eigenvalues of a matrix at once. The video explores the interesting mathematical structure behind the QR algorithm, and presents a Python example to demonstrate it in practice.
For more information see the main course website at people.math.wisc.edu/~chr/am205
@felixyeung8844 8 ай бұрын
Very helpful!
@tobiassugandi 3 ай бұрын
great lecture and very elegant algorithm! Would be much easier to understand if the notation for the Rayleigh Quotient Matrix is NOT A_k since they are NOT A, but much closer to the diagonal matrix D
@chrisrycroft2010 3 ай бұрын
Thanks for the feedback and that is a good observation. I've always found this algorithm difficult to explain, given the similar definitions of the Q_k, R_k, and the underscored versions. You make a good point about A_k becoming close to diagonal. One counterpoint is that A_0 does exactly match A. But I think you're right, that some other notation might be more appropriate to indicate how it behaves in the limit.
Chris Rycroft
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Chris Rycroft
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